Equation 677 Database

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Magma b0482f70dccf…

magma b0482f70dccf
Size
381
Isomorphism class hash
b0482f70dccf8e4b816d594dd47857c500ebcc0e13b57829cd5aa08dee0aeade
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:47:45
Display reorder
380,241,230,220,260,271,250,216,8,205,73,72,124,235,245,225,266,276,256,67,68,66,70,71,69,181,186,177,197,286,191,95,290,94,92,93,91,323,324,325,326,327,328,32,30,31,29,96,28,165,170,281,150,156,161,99,98,97,210,100,203,62,61,296,64,65,63,356,360,341,336,350,331,366,349,371,375,240,231,221,261,270,251,217,128,207,127,126,129,237,247,227,267,277,257,10,11,9,13,125,12,182,189,176,196,287,192,75,291,74,77,78,76,321,322,320,319,329,318,53,54,55,56,57,58,166,171,280,151,155,160,60,59,102,211,101,204,15,14,297,17,18,16,357,361,340,337,351,330,367,346,370,377,243,233,223,263,273,253,218,138,208,137,136,139,238,248,228,268,278,258,33,34,35,36,135,37,180,187,175,198,288,193,107,293,106,104,105,103,300,302,301,304,305,303,109,110,108,112,113,111,168,173,283,153,158,163,0,3,2,213,4,200,134,133,298,130,131,132,358,363,343,338,353,333,368,347,373,378,242,232,222,262,272,252,215,123,206,122,120,121,236,246,226,265,275,255,41,42,40,39,119,38,183,185,178,195,285,190,84,292,83,81,82,80,309,310,311,306,307,308,86,87,85,89,90,88,167,172,282,152,157,162,6,5,7,212,1,201,118,117,295,114,115,116,355,362,342,335,352,332,365,345,372,376,244,234,224,264,274,254,219,148,209,147,146,149,239,249,229,269,279,259,79,25,24,27,145,26,184,188,179,199,289,194,144,294,143,141,142,140,312,313,314,315,316,317,47,48,46,44,45,43,169,174,284,154,159,164,52,51,50,214,49,202,20,19,299,22,23,21,359,364,344,339,354,334,369,348,374,379 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = magma#e6667989dcd92e07f9ac29d8b243d6a96a38fa8a609415f393f811e1aaa26c76, M = {67} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + x + 1); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. Equation 255: satisfied. Idempotent elements: 51.

last edited by qawbecrdtey at 2026-10-01 23:47:46 · history